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CLOSE BINARY MODELS for LUMINOUS BLUE VARIABLE STARS J. S. GALLAGHER Lowell Observatory 1400 West Mars Hill Road Flagstaff, Ariz

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CLOSE BINARY MODELS for LUMINOUS BLUE VARIABLE STARS J. S. GALLAGHER Lowell Observatory 1400 West Mars Hill Road Flagstaff, Ariz CLOSE BINARY MODELS FOR LUMINOUS BLUE VARIABLE STARS J. S. GALLAGHER Lowell Observatory 1400 West Mars Hill Road Flagstaff, Arizona 86001 U.S.A. ABSTRACT. The evolution of massive close binary stars inevitably involves mass exchange between the two stellar components as well as mass loss from the system. A combination of these two processes could produce the stellar wind-modulated behavior seen in LB Vs. The possibility that LBVs are powered by accretion is examined, and does not appear to be a satisfactory general model. Instead, identification of LBVs with close binaries in high mass-loss rate or common envelope evolutionary phases shows promise. 1. Introduction This conference has raised a variety of unanswered questions concerning luminous blue variable stars (hereafter LBVs). What physical class of star are they? Why does an unstable phase occur for only a fraction of evolved very luminous stars? How does the instability process operate and for how long? In this review I briefly consider one set of answers; i.e., that some LBVs are produced by the evolution of massive binary stars. Invocation of binary star evolution is justified by prior experience when dealing with unusual stellar characteristics that apply only to a subset of stars in a given physical class. Examples of successful applications of binary models to peculiar classes of stars include classical, recurrent, and dwarf novae; symbiotic stars: barium stars; and luminous x-ray stars. But there is a price to be paid when including binaries. The evolutionary function E of a single massive star can be represented to zero order as E(MQ, t, z, Mw(t),L(t),B(t)), where Mo is the initial mass, 2 the mean metallicity, Mw(t) the wind mass-loss rate, L the angular momentum, and B the average magnetic field strength. This is bad enough! However, the evolutionary function for binaries is even more complex as all of the above terms now apply to both members of the binary, and additional terms relating to orbital period, mass ratio time, and accretion rates (all functions of time) must be added (e.g., Eggleton 1985). The daunting complexity of binary evolution has caused some people to decide that this problem is simply a cleverly disguised opportunity for theorists (and enterprising observers) to ascend into free-parameter heaven. This view, whatever its merits, ignores the fact that many massive stars are members of binaries where interactions must occur during the normal course of evolution. Several arguments suggest that binary evolution is relevant to the existence of LBVs: (1) At least 40% of massive stars are born in binary star systems with some potential for 185 K. Davidson et al. (eds.), Physics of Luminous Blue Variables, 185-194. © 1989 by Kluwer Academic Publishers. Downloaded from https://www.cambridge.org/core. IP address: 170.106.202.58, on 30 Sep 2021 at 10:22:53, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0252921100004449 186 binary interaction during their lifetimes (cf. Garmany et al. 1980). (2) There is a proven tendency for interacting binary stars to experience episodic outbursts with mass ejection from the system. (3) The lowered gravitational potentials at the surfaces of near Roche- lobe filling members of binary systems should lead to enhanced mass-loss rates even during quiescent phases. (4) The evolution of binary stars takes place over longer time scales than those of single stars of similar mass. These features imply that processes due to the presence of massive binaries will affect only part of the massive star stellar population, are likely to be associated with episodic mass ejections and high mass-loss rates, and may occur in older environments than those where massive single stars are found. Binary stars must be included in possible models for LBVs, as LBVs share all of the above symptoms of ongoing binary star evolution. 2. Accretion-Powered Binary Model Theoretical models and observations both support the view that mass ejection events and bolometric luminosity variations can be produced by accretion within binary star systems. This aspect of binary systems is perhaps most clearly illustrated by outbursts in symbiotic stars, where disk accretion is often the physical cause of eruptive behavior (cf. Kenyon 1986). t Figure 1. Schematic model of a massive binary system with disk accretion (Kenyon and Gallagher 1985). In a key paper, Bath (1979; see also Webbink 1979) suggested that the accretion model be extended to the LBVs. The disk accretion model is schematically illustrated in Figure 1, which is reproduced from Kenyon and Gallagher (1985). Bath assumed an a Downloaded from https://www.cambridge.org/core. IP address: 170.106.202.58, on 30 Sep 2021 at 10:22:53, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0252921100004449 187 disk to estimate temperatures of the accreting system and used simple potential energy arguments to derive an accretion luminosity La, GMMa ./ La % 10 —R~ * IIOOOJ (6 x 10-3) w' _1 _1 Here veac is in km s , and Ma is in units of Af© yr . The last term in this expression is -1 cause for concern. Unless a compact object is allowed such that vesc > 600 km s , then very high accretion rates are required to achieve luminosites in the LBV range. A compact accretor, however, is unlikely to power most in LBVs. The minimum mass of the accreting object can be estimated from the Eddington luminosity LE = 3 X 104(Af/Af©) £©, where M is the mass of the accreting star. For an LBV luminosity of iboi > 3 x 105 Z®, the accreting star should have a mass of Af > 10Af©, which exceeds the masses of all but the most extreme stellar black holes. 4.4 4.8 log T^ K Figure 2. Luminosity-temperature curves for Bath (1979) accretion models. The tracks are labeled by the mass of the accreting star. A lower bound is set when the disk becomes optically thin and the upper bound by La > LE- A second difficulty is illustrated in Figure 2, which is based on Bath (1979). For a system in which the accretion disk is a major luminosity source, temperature will increase w with Ma\ e.g., in Bath's model Tmax a M2 with 7 0.25. The behavior of this model is inconsistent with the observations showing that LBVs reach maximum visual luminosity at minimum temperature and the evidence for roughly constant £boi in LBVs. These prop­ erties are most readily understood in terms of variations in Mw which effect the location of the pseudophotosphere and thus Lvi8, behavior which is well-documented in the early post-maximum development of classical novae (Gallagher and Code 1974; Ruggles and Bath 1979). Disk accretion models do not seem to fully explain LBVs. Thus Figure 1 might be representative of a quiescent phase LBV where stellar photospheres and the disk all Downloaded from https://www.cambridge.org/core. IP address: 170.106.202.58, on 30 Sep 2021 at 10:22:53, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0252921100004449 188 contribute to the visual luminosity, while the disk is also responsible for extra line emission. Detailed comparisons with observations are necessary to see if even this scaled-down disk accretion model is acceptable. An alternate version of this model is possible if LBVs are experiencing saturated accretion; i.e., if La > LE- We then can ask whether the wind would carry the excess La, as suggested by Zytkow's (1973) and Kato's (1985) models. The Eddington limit provides ' a natural reason for near constant ibol from the system, and fluctuations in Mw are likley \ to occur and produce the desired visual light variations. We could consider these types of ' objects as "stealth" binaries, since the binary nature of the underlying system is largely but '• not completely optically obscured by a pseudophotosphere associated with the accreting star. ; -3 -1 We require very high accretion rates of Ma > 6 x 1O M0 yr to produce a hidden ; binary from a system where the accretor is a main-sequence star. It is fair to ask if such high rates can be expected in nature. Webbink (1985) has emphasized that there are three J natural time scales associated with the mass-losing star which can drive accretion rates in i binaries. As a rough estimate of allowable rates for each time scale r; from a star of mass 1 Mo with available mass fraction / for mass loss, we have Ma(i) « fMoT^ . Even for a 6 -4 -1 massive star, nuclear time scales are > 10 yr, so we expect Ma(nuc) < 10 M© yr '. Thermal time scales are similar, so we must rely on the dynamical time scale to produce Eddington-critical accretion rates. Accretion on dynamical time scales occurs when a star cannot readjust to the changes in Roche lobe size in an interacting binary, and in principle can produce the required high values of Ma. A detailed study of this problem is in progress as M. S. Hjellming's Ph.D. thesis at the University of Illinois (see Hjellming and Webbink 1987). However, stars with convective envelopes are known to be unstable against dynamical mass exchange, and thus a cool supergiant donor is a good candidate for the model. Possibly stars near the Eddington limit are also sufficiently unstable to make this mechanism work (cf. McClusky and Kondo 1976). A problem that remains to be resolved is the response of the accreting star to rapid accretion.
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